Map Projection

A Guide to the Mathematics of Map Projections
A technical paper (47 pages) on the mathematics of map projections with particular emphasis on the transverse Mercator projection and Redfearn’s equations. This paper was presented at the Victorian Tasmanian Survey Conference: Across the Strait, Launceston, Tasmania, 15-17 April, 2004.
A GUIDE TO MAP PROJECTIONS V3.pdf

Map Projection Theory
Lecture notes on the theory of map projections (two parts, 41 + 10 pages).
MapProjectionTheory_1.pdf
MapProjectionTheory_2.pdf

Minimum Error Map Projection for Victoria
A technical paper presented at the FIG XX International Conference (Commission 5), Melbourne, Victoria, 5-12 March, 1994 (13 pages)
Minimum Error projection for Victoria.pdf

Some Applications of Clenshaw’s Recurrence Formula in Map Projections
A technical paper (34 pages) providing a detailed discussion of Clenshaw’s recurrence formula and associated summation algorithm with applications in map projections. In particular, computation of meridian distance on the ellipsoid and transformations between the ellipsoid and the Transverse Mercator projection. Matlab functions included.
Clenshaw_Map_Projections_V2.pdf

The Gauss-Krüger Projection
A technical paper (20 pages) by R.E. Deakin, M.N. Hunter and C.F.F. Karney on the Gauss-Krüger projection and Krüger’s equations (series method). This paper was presented at the 23rd Victorian Regional Survey Conference, Warrnambool, 10-12 September, 2010.
Gauss-Krueger Warrnambool Conference.pdf

The Gauss-Krueger Projection: Karney-Krueger equations
A technical paper (22 pages) by R.E. Deakin, M.N. Hunter and C.F.F. Karney on the Gauss-Krueger projection and the Karney-Krueger equations. This paper was presented at the 25th International Cartographic Conference, Paris, 3-8 July, 2011.
Gauss-Krueger Paris Conference.pdf

A Fresh Look at the UTM Projection: Karney-Krueger equations
A technical paper (19 pages) by R.E. Deakin, M.N. Hunter and C.F.F. Karney on the Transverse Mercator (Gauss-Krueger) projection and the Karney-Krueger equations. This paper was presented at the Surveying and Spatial Sciences Institute (SSSI) Land Surveying Commission National Conference, Melbourne, 18-21 April, 2012. This paper is an updated version of the Warrnambool Conference paper above.
A fresh look at the UTM projection – the Karney-Krueger equations.pdf

Map Projections, Mathematics and Computers
A technical paper (12 pages) describing how Computer Algebra Systems (CAS) are used to develop new equations for the Transverse Mercator projection. This paper was presented at the Geospatial Science Research_1 conference, Melbourne, 12-14 December, 2011.
MATHEMATICS AND MAP PROJECTIONS(GEOM2093).pdf

Tilted Camera map projection
Tilted Camera Map Projection.pdf

Transverse Mercator Projection: Karney-Krueger equations
These notes (12 pages) set out in detail the Forward and Inverse transformations between geographic coordinates (φ,λ) and grid coordinates (E,N) of the transverse Mercator projection of the ellipsoid using the Karney-Krueger equations. Equations for Grid Convergence and Point Scale Factor are also given for both transformations. An Excel workbook has spreadsheets for both transformations
Karney-Krueger equations.pdf
Karney-Krueger.xlsx